Patrick Stevens

I was recently having a late-night argument with someone about the following thesis:

If you can’t explain something in a simple way, you don’t understand it.

They were using this to argue something like the following:

Jargon is unhelpful because it sets a very high barrier for entry into any field.

My reply, as something of a mathematician, is as follows.

While there are certainly more accessible parts of physics and maths which can be well-explained by analogies and imprecise language
(and, indeed, we often use them to students, and Brian Cox tries to use them in e.g. documentaries),
it has led to the horrible nightmare which is everyone thinking wrongly that they understand quantum mechanics [QM] because they heard some cool analogies.
QM has very little in common with its analogies;
the analogies are basically just there to give an idea that “things are weird, classical intuition will fail”.
It’s the flip side to “if you use abstruse language then you create an environment where you must pass the initiation tests to take part”:

If you use imprecise language then you create an environment where everyone thinks they understand but they’re all wrong.

Both approaches have merits, and boringly the correct answer is probably “use a mixture of the two, with the ratio depending on appropriateness to the subject”.
However, physics is increasingly a subfield of maths since the advent of QM and general relativity (which are purely mathematical frameworks),
and in maths we find the precise language extremely important because we strive for total rigour in this, the only subject where it’s actually possible.
Most people start doing maths without access to the language,
and they often find lots of interesting stuff
(Ramanujan is a particular example of such a mathematician,
who did a lot of great work before ever interacting with Western mathematicians),
but once you know the language, the language creates a framework which goes some way to guaranteeing the correctness of your results and which can help you spot connections/see more patterns.

From a maths point of view, documentaries are there to get people interested in playing around for themselves,
rather than to actually impart mathematical knowledge.
In an ideal world, I think we’d let people discover loads of maths on their own,
and then show them the precise framework and language it fits into,
but there just isn’t time,
so we teach it by shoving the framework down students’ throats until they either give up maths or become divinely inspired and start playing with it for themselves.
Additionally a lot of the maths I study [though this might be historical accident,
derived from our tradition of using jargon] consists of the study of objects which have very few properties, so they defy analogy.

Sometimes it turns out that a certain collection of “very few properties”,
like the collection by which we define the objects we call groups,
happen to capture a certain intuition
(in this case, the idea of “symmetry” turns out in a deep way to be precisely captured by groups).
However, that seems like being the exception rather than the rule,
and a general collection of “few properties” won’t have a neat accessible analogy that anyone has been able to find.
Especially when you study metamathematics, as well,
some very deep theorems turn out to hinge on exactly what you mean by “the integers” or “the real numbers” or whatever.
In such fringe cases it is absolutely necessary to be totally precise that we mean “the integers” in a specific technical sense rather than “the integers” as a fuzzy concept,
or else one will almost certainly go wrong.

So there are definitely cases where the “stupid jargon” is necessary to maintain clarity of thought.
(Some such theorems do actually impinge on reality, too! Usually via computer science.)